Lyapunov Stability Research Papers - Academia.edu (original) (raw)

In this paper, we study the stability problem of nonlinear dynamical control systems. We consider continuous-time dynamical systems whose nominal part is stable and whose perturbed part (uncertainties) is norm-bounded by a positive... more

In this paper, we study the stability problem of nonlinear dynamical control systems. We consider continuous-time dynamical systems whose nominal part is stable and whose perturbed part (uncertainties) is norm-bounded by a positive function. Under some conditions on the perturbation, by using Lyapunov techniques, we show that the system can be uniformly asymptotically stable by a continuous controller.

Abstract: In this paper, we investigate the control and reduced-order synchronization in a new third-order chaotic system derived from the rigid body dynamics. A recursive backstepping control is designed based on Lyapunov stability... more

Abstract: In this paper, we investigate the control and reduced-order synchronization in a new third-order chaotic system derived from the rigid body dynamics. A recursive backstepping control is designed based on Lyapunov stability theory to eliminate the chaotic behaviour. To ...

—A deterministic epidemiological model describing the spread of infectious disease characterized by pseudo-recovery due to incomplete treatment is studied. The resulting SEIRI model in a closed system is robustly analysed. Trans-critical... more

—A deterministic epidemiological model describing the spread of infectious disease characterized by pseudo-recovery due to incomplete treatment is studied. The resulting SEIRI model in a closed system is robustly analysed. Trans-critical bifurcation at the threshold, R0 = 1, is investigated and the global asymptotic dynamics of the model around the disease-free and endemic equilibria are explored by the aid of suitable Lyapunov functionals. Further, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behaviour of the system.

A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the... more

A neural network control scheme with an adaptive observer is proposed in this paper to Quadrotor helicopter stabilization. The unknown part in Quadrotor dynamical model was estimated on line by a Single Hidden Layer network. To solve the non measurable states problem a new adaptive observer was proposed. The main purpose here is to reduce the measurement noise amplification caused by conventional high gain observer by introducing some changes in observer's original structure that can minimize the variance and the amplitude of the noisy signal without increasing tracking error. The stability analysis of the overall closed-loop system/ observer is performed using the Lyapunov direct method. Simulation results are given to highlight the performances of the proposed scheme.

This paper proposes a sensorless sliding mode control (SMC) for a five phase permanent magnet synchronous motor (PMSM) based on a sliding mode observer (SMO). The stability of the proposed strategy is proved in the sense of the Lyapunov... more

This paper proposes a sensorless sliding mode control (SMC) for a five phase permanent magnet synchronous motor (PMSM) based on a sliding mode observer (SMO). The stability of the proposed strategy is proved in the sense of the Lyapunov theory. The sliding mode controller is designed with an integral switching surface and the sliding mode observer is developed for the estimation of rotor position and rotor speed. The proposed sensorless control strategy exhibits good dynamic response to disturbances. Simulation results are provided to prove the effectiveness of the proposed strategy.

This paper studies the synchronization dynamics of two linearly coupled parametrically excited oscillators. The Lyapunov stability theory is employed to obtain some sufficient algebraic criteria for global asymptotic stability of the... more

This paper studies the synchronization dynamics of two linearly coupled parametrically excited oscillators. The Lyapunov stability theory is employed to obtain some sufficient algebraic criteria for global asymptotic stability of the synchronization of the systems, and an estimated critical coupling, k cr, for which synchronization could be observed is determined. The synchronization transition is found to be associated with the boundary crisis of the chaotic attractor. In the bistable states, where two asymmetric T-periodic attractors co-exist, we show that the coupled oscillators can attain multi-stability via a new dynamical transition—the basin crisis wherein two co-existing attractors are destroyed while new co-existing attractors are created. The stability of the steady states is examined and the possible bifurcation routes identified.

In recent years, remotely operated vehicles (ROVs) play an important role in various underwater operations. In many applications, ROVs will need to be capable of maneuvering to any given point, following the object and to be controllable... more

In recent years, remotely operated vehicles (ROVs) play an important role in various underwater operations. In many applications, ROVs will need to be capable of maneuvering to any given point, following the object and to be controllable from the surface. The Department of Mechanical Engineering of the University of Guilan designed and fabricated an ROV for underwater exploration with special

This paper deals with the communication problem in the distributed system, considering the limited battery power in the wireless network and redundant transmission among nodes. We design an event-triggered model predictive control... more

This paper deals with the communication problem in the distributed system, considering the limited battery power in the wireless network and redundant transmission among nodes. We design an event-triggered model predictive control (ET-MPC) strategy to reduce the unnecessary communication while promising the system performance. On one hand, for a linear discrete time-invariant system, a triggering condition is derived based on the Lyapunov stability. Here, in order to further reduce the communication rate, we enforce a triggering condition only when the Lyapunov function will exceed its value at the last triggered time, but an average decrease is guaranteed. On the other hand, the feasibility is ensured by minimizing and optimizing the terminal constrained set between the maximal control invariant set and the target terminal set. Finally, we provide a simulation to verify the theoretical results. It's shown that the proposed strategy achieves a good trade-off between the closed-loop system performance and communication rate.

This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the... more

This paper presents the stability analysis of polynomial fuzzy-model-based (PFMB) control system, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB control system is not required that the polynomial fuzzy controller shares the same premises membership functions as those of the polynomial fuzzy model. Piecewise linear membership functions are employed to approximate the membership functions of the polynomial fuzzy model and polynomial fuzzy controller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear membership functions offer a nice property that the grades of membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear membership functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear membership functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB control systems with the specified piecewise linear membership functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.